no they will not give you more money from SSI when you not live with ur parents anymore. I lived with my mom, I had my ssi whole my life since I was born, gain little bit every years on January. Then I moved out of my mom's house, my ssi still the same. Ssi knows I moved to my own place, nothing change my ssi.
If your parents retired, you can ask SSI about their retired, if you can change it to SSDI, get more money. Or you used to work before, then ask for SSDI..SSI is small amount than SSDI or SSA. grr. my dad still works for 30 years, and still counting. When he's retired. I'll try ask for SSDI..hehe.